2022 年 74 巻 2 号 p. 333-352
A method of proving Hardy's type inequality for orthogonal expansions is presented in a rather general setting. Then, sharp multi-dimensional Hardy's inequality associated with the Laguerre functions of convolution type is proved for the type index 𝛼 ∈ [−1/2, ∞)𝑑. The case of the standard Laguerre functions is also investigated. Moreover, the sharp analogues of Hardy's type inequality involving 𝐿1 norms in place of 𝐻1 norms are obtained in both settings.
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